Reinterpretation and Simplified Implementation of a Discontinuous Galerkin Method for Hamilton-Jacobi Equations

摘要

In this talk, we reinterpret a discontinuous Galerkin method originally developed by Hu and Shu for solving Hamilton-Jacobi equations. By this reinterpretation, numerical solutions will automatically satisfy the curl-free property of the exact solutions inside each element. This new reinterpretation allows a method of lines formulation, which renders a more natural framework for stability analysis. Moreover, this reinterpretation renders a significantly simplified implementation with reduced cost, as only a smaller subspace of the original solution space in the original discontinuous Galerkin method is used and the least square procedure used before is completely avoided. We will start the talk with a general description of the discontinuous Galerkin method and its application to Hamilton-Jacobi equations, and end the talk with several numerical results.